The goal of this mini-symposium (split into two parts) is to present state of the art results, on both theoretical guarantees and numerical algorithms, for inverse problems regularization using low complexity models (sparsity, bounded variation, low rank, etc.). These results attempt to bridge the gap between the surprising efficiency of recent regularization methods, and our theoretical understanding of their super-resolution effectiveness. While many theoretical guarantees rely on uniform analysis with with hypotheses requiring randomness or global incoherence of the measurements, real-life problems in imaging sciences (e.g. deconvolution, tomography, MRI, etc.) require more intricate theoretical tools and algorithms to capture the geometry of signals and images that can be stably recovered. This includes for instance variational methods over spaces of measures (e.g. sum of Dirac measures, bounded variation functions, etc.) and the development of novel recovery algorithms that can cope with the strong coherence of the measurement operator. The mini-symposium will gather talks by leading experts in the field.
Organizers:
Jalal Fadili
CNRS-ENSICAEN-Univ. Caen, France
Gabriel Peyré
CNRS-Univ. Paris Dauphine, France